Have you stabilized the tee-shirts with something, interfacing or whatever? It seems like cutting a knit might be easier after it is stabilized.
I like to do my cutting on the floor. If your knees allow, that might be part of the answer. I put a knee on the ruler and it helps keep it firmly anchored where I put it.
Maybe you can use some of the scraps of tee shirts already cut to practice cutting some more on?